Reply to Compton et al.: Another paradoxical misunderstanding

Abstract

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Phylogenetic statistical methods provide an opportunity to formally test the relationship between phenotypic traits (1). When used correctly, phylogenetic models offer powerful insight into the emergence of adaptive trends across evolutionary time (2). Unfortunately, Compton et al. (3) demonstrate how methodological misunderstandings can lead to incorrect interpretations and inaccurate conclusions.

Compton et al. (3) suggest that modeling tumor prevalence (count data) via a Poisson regression model as a function of the number of necropsies, and other covariates, implies that all species have the same rate of cancer. The claim that by instead modeling tumor prevalence divided by the number of necropsies as a proportion, it is possible to account for different intrinsic rates of cancer. However, not only does this approach violate the underlying assumptions of phylogenetic generalized least squares (PGLS) (4), but it also fails to capture variation in intrinsic cancer rates as Compton et al. suggest (3). Note that this is the case even after arcsine transformation—which is widely recognized as inappropriate for analyzing proportional data even in nonphylogenetic context (5). PGLS assumes Brownian-motion trait evolution with a single estimated variance (σ^2^), implying a shared evolution rate across all species (6, 7). Because Compton et al. use such a model (3), their claim that their approach captures difference in intrinsic cancer rates lacks methodological support.

To study tumor prevalence as a proportion in the way Compton et al have done previously (8), it would be most appropriate to use a binomial or beta-binomial regression framework (9). Indeed, when we use a phylogenetic beta-binomial regression on the proportion data, we recover results consistent with Butler et al. (2) (Table 1), confirming that the conclusions are robust to whether tumor prevalence is modeled as counts or proportions.

Compton et al.’s response (3) implies that they are considering a series of multiple pairwise regressions with each covariate separately as equivalent to a multiple regression analysis. However, unlike such pairwise comparisons, in a multiple regression model, the effects of body size, rate of body size evolution, and lineage diversification on tumor prevalence are estimated simultaneously. This apparent misunderstanding of the type of multiple regression analysis utilized by Butler et al. (2) is further illustrated by Compton et al.’s (3) inaccurate assertion that predictors “add or subtract a fixed number.” In multiple regression models, the effect of each covariate is estimated conditional on all other covariates; for example, the body size effect is estimated conditional on the rate of body size evolution. This conditional interpretation is a core strength of multiple regression and allows multiple hypotheses to be evaluated simultaneously. As a result, interaction terms between necropsy number and other covariates are neither required nor meaningful, because necropsy number enters the model as sampling effort rather than as a biological predictor.

We are pleased that Compton et al. agree that our findings are important additions to the study of comparative oncology (3). However, this exchange highlights the necessity of aligning statistical models with the structure of the data and the biological questions at hand, rather than assuming that one-size-fits-all methods that risk obscuring meaningful evoution signal.